Equilibration of isolated macroscopic quantum systems

TL;DR

This paper studies how isolated macroscopic quantum systems tend to reach equilibrium states where deviations become practically unmeasurable over time, under certain conditions on initial states and energy level degeneracies.

Contribution

It extends previous work on quantum equilibration by analyzing large, possibly infinite-dimensional systems with specific energy degeneracy constraints.

Findings

Demonstrates conditions for equilibration in macroscopic quantum systems

Extends theoretical framework beyond finite-dimensional models

Identifies key energy degeneracy conditions for equilibration

Abstract

We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The main requirements are that the initial state, possibly far from equilibrium, exhibits a macroscopic population of at most one energy level and that degeneracies of energy eigenvalues and of energy gaps (differences of energy eigenvalues) are not of exceedingly large multiplicities. Our approach closely follows and extends recent works by Short and Farrelly [2012 New J. Phys. 14 013063], in particular going beyond the realm of finite-dimensional systems and large effective dimensions.